Without using Lax pairs, the FL equation (REF ) was bilinearized and
determinantal solutions of the bilinear FL equations were constructed in a delicate direct way
by introducing determinants of the Cauchy matrix type [1]}, [2]}.
Another direct approach was presented in [3]},
where a chain of Bäcklund transformations of the pKN\((-1)\)  () was constructed and viewed
as semi-discrete equations in the Merola-Ragnisco-Tu hierarchy (cf.[4]})
and solutions of the FL equation (REF ) were given in term of Cauchy matrix
by using connection between the Merola-Ragnisco-Tu hierarchy and the Ablowitz-Ladik hierarchy.
From the bilinear form given in [1]} it is easy to get 3-soliton solution
in terms of Hirota's polynomials of exponential functions [6]}.
However, it is difficult to give double Wronskian solutions to those FL equations.
As a matter of fact, Eqs.() is the potential form KN\((-1)\)  (i.e. the first negative member in the KN hierarchy,
see Eq.(REF )).
To our understanding, it is difficult to express the integral \(u=\partial ^{-1}_x q\)  in terms of double Wronskians.
